ThetaBank's default risk assessment involves calculating the joint probability of default for the two mortgage companies and comparing it to the independent risk model.

Individual Exposure at Default (EAD):$20 million for each mortgage company.

Loss Given Default (LGD):100%

Probability of Default (PD):10% for each mortgage company.

Joint Probability of Default:5%

For independent risks, the joint probability of default for two independent events is the product of their individual probabilities:

\text{Joint Probability (Independent)} = PD_1 \times PD_2 = 0.10 \times 0.10 = 0.01 \text{ (or 1%)}

Given that ThetaBank predicts the joint probability at 5%, the independent model would have underestimated the actual probability by:

5%−1%=4%5%−1%=4%

Therefore, the underestimated probability is:

4%−2%=2%4%−2%=2%

References

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